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Algebra 5
DecisionProblemsinGroupTheory(L24)................. .............5
LieAlgebrasandRepresentationTheory(M24)............ ...............5
ModularRepresentationsofFiniteGroups(L24).......... ................6
Calculusandalgebra(L24)............................ ..........8
Representationsof?nitegroupsofLietype(L24)......... .................8
CommutativeAlgebra(M24)............................ .........9
Non-commutativealgebras(L24)....................... ............9
VonNeumannAlgebras(L24)............................ .........10
Analysis 12
TopologicalGroups(L24)............................. ..........12
TopicsinIn?niteGroups(M16)......................... ...........12
AnalysisontheDiscreteHypercube(L24)— Non–Examinable .................13
IntroductiontoFunctionalAnalysis(M24).............. ................14
ComplexDi?erentialEquations(L24)................... .............15
Ellipticpartialdi?erentialequations(M24)........... ..................15
Combinatorics 17
Combinatorics(M16)................................. .........17
CombinatorialProbability(L16)...................... .............17
HypergraphGames(E8)— Non–Examinable ..........................18
ArithmeticCombinatorics(M16)....................... ............18
GeometryandTopology 19
TheX-raytransformingeometryanddynamics(L24)........ ...............19
AlgebraicTopology(M24)............................. ..........20
Di?erentialGeometry(M24)........................... ..........20
SpectralGeometry(L24).............................. .........21
AlgebraicGeometry(M24)............................. .........22
ComplexManifolds(L24).............................. .........22
AlgebraicGroups(M24)............................... .........24
FibreBundles(L16).................................. ........24
AlgebraicCycles(L24)............................... ..........25
Logic 26
CategoryTheory(M24)................................ ........26
SetTheoryandLogic(L24)............................. .........27
NumberTheory 29
EllipticCurves(L24)................................ ..........29
LocalFields(M16)................................... ........29
ErgodicTheory(L24)................................. ........30
TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24).............31
AlgebraicNumberTheory(M16)......................... ..........31
ModularFormsandAutomorphicForms(L24)............... ............32
Non-abelianLubin-Tatetheory(M24)— Non–Examinable ...................32
Probability 3
AdvancedProbability(M24)........................... ..........3
StochasticNetworks(L24)............................ ...........3
StochasticLoewnerEvolutions(L16)................... ..............3
StochasticCalculusandApplications(L24)............. ................3
ParticlePhysics,QuantumFieldsandStrings 46
QuantumFieldTheory(M24)............................ .........46
SymmetryandParticlePhysics(M24).................... ............47
StatisticalFieldTheoryandApplications(M24)......... .................48
AdvancedQuantumFieldTheory(L24).................... ...........49
StringTheory(L24).................................. ........49
SupersymmetryandExtraDimensions(L24)............... .............50
StandardModel(L24)................................. ........51
SolitonsandInstantons(E16)......................... ............52
Supergravity(E16).................................. .........53
3
QuantumInformationandQuantumFoundations 54
IntroductiontoQuantumComputation(M16).............. .............54
QuantumInformation,EntanglementandNonlocality(M16). ..................55
PhilosophyofClassicalandQuantumMechanics(M12,L12).. .................55
MathematicalAspectsofQuantumInformationTheory(L24). ..................56
QuantumControl(L16)................................ ........57
RelativityandGravitation 59
Cosmology(M24)..................................... .......59
GeneralRelativity(M24)............................. ..........61
AdvancedCosmology(L16)............................. .........62
ApplicationsofDi?erentialGeometrytoPhysics(L24).... ...................63
BlackHoles(L24).................................... .......64
QuantumCosmology(E16).............................. ........65
IntroductionToTwistorTheory(E16)................... ............66
Astrophysics 67
AstrophysicalFluidDynamics(M24).................... .............67
StructureandEvolutionofStars(M24).................. .............68
AccretionDiscs(L16)................................ .........68
Galaxies(L24)...................................... .......69
PhysicalCosmology(L24)............................. ..........70
StellarandPlanetaryMagneticFields(L24)............. ................71
I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.
So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?
What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?
Please help me I am clueless.
I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).
Thank you for your help. :)
DecisionProblemsinGroupTheory(L24)................. .............5
LieAlgebrasandRepresentationTheory(M24)............ ...............5
ModularRepresentationsofFiniteGroups(L24).......... ................6
Calculusandalgebra(L24)............................ ..........8
Representationsof?nitegroupsofLietype(L24)......... .................8
CommutativeAlgebra(M24)............................ .........9
Non-commutativealgebras(L24)....................... ............9
VonNeumannAlgebras(L24)............................ .........10
Analysis 12
TopologicalGroups(L24)............................. ..........12
TopicsinIn?niteGroups(M16)......................... ...........12
AnalysisontheDiscreteHypercube(L24)— Non–Examinable .................13
IntroductiontoFunctionalAnalysis(M24).............. ................14
ComplexDi?erentialEquations(L24)................... .............15
Ellipticpartialdi?erentialequations(M24)........... ..................15
Combinatorics 17
Combinatorics(M16)................................. .........17
CombinatorialProbability(L16)...................... .............17
HypergraphGames(E8)— Non–Examinable ..........................18
ArithmeticCombinatorics(M16)....................... ............18
GeometryandTopology 19
TheX-raytransformingeometryanddynamics(L24)........ ...............19
AlgebraicTopology(M24)............................. ..........20
Di?erentialGeometry(M24)........................... ..........20
SpectralGeometry(L24).............................. .........21
AlgebraicGeometry(M24)............................. .........22
ComplexManifolds(L24).............................. .........22
AlgebraicGroups(M24)............................... .........24
FibreBundles(L16).................................. ........24
AlgebraicCycles(L24)............................... ..........25
Logic 26
CategoryTheory(M24)................................ ........26
SetTheoryandLogic(L24)............................. .........27
NumberTheory 29
EllipticCurves(L24)................................ ..........29
LocalFields(M16)................................... ........29
ErgodicTheory(L24)................................. ........30
TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24).............31
AlgebraicNumberTheory(M16)......................... ..........31
ModularFormsandAutomorphicForms(L24)............... ............32
Non-abelianLubin-Tatetheory(M24)— Non–Examinable ...................32
Probability 3
AdvancedProbability(M24)........................... ..........3
StochasticNetworks(L24)............................ ...........3
StochasticLoewnerEvolutions(L16)................... ..............3
StochasticCalculusandApplications(L24)............. ................3
ParticlePhysics,QuantumFieldsandStrings 46
QuantumFieldTheory(M24)............................ .........46
SymmetryandParticlePhysics(M24).................... ............47
StatisticalFieldTheoryandApplications(M24)......... .................48
AdvancedQuantumFieldTheory(L24).................... ...........49
StringTheory(L24).................................. ........49
SupersymmetryandExtraDimensions(L24)............... .............50
StandardModel(L24)................................. ........51
SolitonsandInstantons(E16)......................... ............52
Supergravity(E16).................................. .........53
3
QuantumInformationandQuantumFoundations 54
IntroductiontoQuantumComputation(M16).............. .............54
QuantumInformation,EntanglementandNonlocality(M16). ..................55
PhilosophyofClassicalandQuantumMechanics(M12,L12).. .................55
MathematicalAspectsofQuantumInformationTheory(L24). ..................56
QuantumControl(L16)................................ ........57
RelativityandGravitation 59
Cosmology(M24)..................................... .......59
GeneralRelativity(M24)............................. ..........61
AdvancedCosmology(L16)............................. .........62
ApplicationsofDi?erentialGeometrytoPhysics(L24).... ...................63
BlackHoles(L24).................................... .......64
QuantumCosmology(E16).............................. ........65
IntroductionToTwistorTheory(E16)................... ............66
Astrophysics 67
AstrophysicalFluidDynamics(M24).................... .............67
StructureandEvolutionofStars(M24).................. .............68
AccretionDiscs(L16)................................ .........68
Galaxies(L24)...................................... .......69
PhysicalCosmology(L24)............................. ..........70
StellarandPlanetaryMagneticFields(L24)............. ................71
I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.
So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?
What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?
Please help me I am clueless.
I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).
Thank you for your help. :)